I have an Astronomy/Physics question I need answered, any help?

[wnnagetdirrty82787]

The great galaxy of Andromeda has an angular diameter along its long axis of about 5 degrees. Its distance is about 2.2 million light ears. What is its linear diameter?

[Scotty]

You're looking at something 5? wide from where you are, 2.2 million light years away. So it's an isosoles triangle. Bisect it from where you are (the apex) for 2.5? right triangle. Then just use simple right triangle trigonometry.

tan (theta) = opposite side ÷ adjacent side.
opposite side = tan (theta) x adjacent side.
tangent 2.5?(2.2 x 10^6) = 1/2 of your answer

answer = 192,108 l.y. or roughly twice the estimated size of the Milky Way. That's assuming it's perpendicular to your line of sight, of course. If you knew the exact angle you could use the law of sines or cosines or one of those laws for a more precise answer.